\(\varphi _i(Fw_i)\)  is a shorthand for the vector \(\bigl [\varphi _i^1(F_1w_i), \ldots , \varphi _i^n(F_nw_i)\bigr ]^\mathsf {T}\) , \(F_j\)  is the \(j\) -th row of the matrix \(F\) , and \(\varphi _i^j:\mathbb {R}\rightarrow \mathbb {R}\)  is any function with \(\sup \limits _{s\in \mathbb {R}}|\varphi _i^j(s)|\le \phi _{\max } \le U_{\rm max}\) . In other words, we have chosen to saturate the measurements that we obtain from the noise input vector before inserting them into our control vector. This way we do not assume that the noise distribution is defined over a compact domain, which is an advantage over other approaches [1]}, [2]}.
Moreover, the choice of element-wise saturation functions \(\varphi _i(\cdot )\)  is left open. As such, we can accommodate standard saturation, piecewise linear, and sigmoidal functions, to name a few.
